library(dplyr)
library(nycflights13)

数据

library(nycflights13)
dim(flights)
[1] 336776     19
data(flights)

dplyr动作

  1. 取行:filter()
  2. 排序: arrange()
  3. 取列: select()
  4. 生成新变量: mutate()
  5. 分组汇总: group_by() %>% summarise()
  6. 动作连贯:%>%: 快捷键: ctrl + shift + M

filter()

dplyr::filter(flights, month ==1, day == 1)

base R 方法

flights[flights$month == 1 & flights$day == 1, ]

arrange()

arrange(flights, year, month, day)
arrange(flights, desc(arr_delay))

取列

select(flights, year, month, day)
select(flights, year:day)
select(flights, -(year:day))
flights %>% select(contains('dep'))

重命名

select(flights, tail_num = tailnum)
rename(flights, tail_num = tailnum)

增添新变量

mutate(flights,
  gain = arr_delay - dep_delay,
  speed = distance / air_time * 60
)
mutate(flights,
  gain = arr_delay - dep_delay,
  gain_per_hour = gain / (air_time / 60)
)
transmute(flights,
  gain = arr_delay - dep_delay,
  gain_per_hour = gain / (air_time / 60)
)

汇总

summarise(flights,
  delay = mean(dep_delay, na.rm = TRUE)
)

抽样

sample_n(flights, 10)
sample_frac(flights, 0.01)

分组

by_tailnum <- group_by(flights, tailnum)
delay <- summarise(by_tailnum,
  count = n(),
  dist = mean(distance, na.rm = TRUE),
  delay = mean(arr_delay, na.rm = TRUE))
delay <- dplyr::filter(delay, count > 20, dist < 2000)

使用连贯动作

detach(dplyr)
Error in detach(dplyr) : 'name'参数不对
flights %>%
  group_by(year, month, day) %>%
  select(arr_delay, dep_delay) %>%
  summarise(
    arr = mean(arr_delay, na.rm = TRUE),
    dep = mean(dep_delay, na.rm = TRUE)
  ) %>%
  filter(arr > 30 | dep > 30)

多变量汇总

daily <- group_by(flights, year, month, day)
(per_day   <- summarise(daily, flights = n()))
(per_month <- summarise(per_day, flights = sum(flights)))
(per_year  <- summarise(per_month, flights = sum(flights)))

多表合并

flights2 <- flights %>% select(year:day, hour, origin, dest, tailnum, carrier)

flights2 %>% 
  left_join(airlines)
Joining, by = "carrier"
data("weather")
weather
flights2 %>% left_join(weather)
Joining, by = c("year", "month", "day", "hour", "origin")

用特定变量合并交集

planes
flights2 %>% left_join(planes, by = "tailnum")

合并变量名称不同?

airports
flights2 %>% left_join(airports, c("dest" = "faa"))

四种合并(join)方式

df1 <- tibble(x = c(1, 2), y = 2:1)
df2 <- tibble(x = c(1, 3), a = 10, b = "a")
df1
df2
  1. inner_join(x, y): xy交集
df1 %>% inner_join(df2)
Joining, by = "x"
  1. left_join(x, y), 保留x的所有观测。最为常见
df1 %>% left_join(df2)
Joining, by = "x"
  1. right_join(),保留y中的所有观测,等同于left_join(y, x),但列的排序稍有不同。
df1 %>% right_join(df2)
Joining, by = "x"
df2 %>% left_join(df1)
Joining, by = "x"
  1. full_join() 保留x, y所有观测,用NA填充。
df1 %>% full_join(df2)

与观测有关的join

  1. semi_join(x, y): 保留y中有匹配的x观测值
  2. anti_join(x, y):将x中与y有匹配的数据全部丢弃
flights %>% 
  anti_join(planes, by = "tailnum") %>% 
  count(tailnum, sort = TRUE)
df1 <- tibble(x = c(1, 1, 3, 4), y = 1:4)
df2 <- tibble(x = c(1, 1, 2), z = c("a", "b", "a"))
df1
df2
df1 %>% nrow()
[1] 4
df1 %>% inner_join(df2, by = "x")
df1 %>% semi_join(df2, by = "x")

集合操作

(df1 <- tibble(x = 1:2, y = c(1L, 1L)))
(df2 <- tibble(x = 1:2, y = 1:2))
intersect(df1, df2)
union(df1, df2)
setdiff(df1, df2)
setdiff(df2, df1)

窗口函数 (window functions)

与mutate和filter结合使用,窗口函数可以大有作为

library(Lahman)
batting <- Lahman::Batting %>%
  as_tibble() %>%
  select(playerID, yearID, teamID, G, AB:H) %>%
  arrange(playerID, yearID, teamID) %>%
  semi_join(Lahman::AwardsPlayers, by = "playerID")

players <- batting %>% group_by(playerID)
players
mutate(players, G_rank = min_rank(G))
# For each player, find the two years with most hits
filter(players, min_rank(desc(H)) <= 2 & H > 0)
# Within each player, rank each year by the number of games played
mutate(players, G_rank = min_rank(G))
# For each player, find every year that was better than the previous year
filter(players, G > lag(G))
# For each player, compute avg change in games played per year
mutate(players, G_change = (G - lag(G)) / (yearID - lag(yearID)))

# For each player, find all where they played more games than average
filter(players, G > mean(G))
# For each, player compute a z score based on number of games played
mutate(players, G_z = (G - mean(G)) / sd(G))
  1. 排序和计算顺序:row_number(), min_rank(), dense_rank(), cume_dist(), percent_rank(), and ntile().
  2. 滞后和领先操作: lead() and lag()

排序

x <- c(1, 1, 2, 2, 2)

row_number(x)
[1] 1 2 3 4 5
min_rank(x)
[1] 1 1 3 3 3
dense_rank(x)
[1] 1 1 2 2 2
cume_dist(x)
[1] 0.4 0.4 1.0 1.0 1.0
#> [1] 0.4 0.4 1.0 1.0 1.0
percent_rank(x)
[1] 0.0 0.0 0.5 0.5 0.5
# select the top 10% of records within each group
filter(players, cume_dist(desc(G)) < 0.1)
by_team_player <- group_by(batting, teamID, playerID)
by_team <- summarise(by_team_player, G = sum(G))
by_team_quartile <- group_by(by_team, quartile = ntile(G, 4))
summarise(by_team_quartile, mean(G))

领先滞后

x <- 1:5
lead(x)
lag(x)
# Compute the relative change in games played
mutate(players, G_delta = G - lag(G))
# Find when a player changed teams
filter(players, teamID != lag(teamID))
---
title: "dplyr介绍"
output:
  html_document:
    df_print: paged
  pdf_document: default
---

```{r}
detach("package:dplyr")
library(dplyr)
library(nycflights13)
```

# 数据
```{r}
library(nycflights13)
dim(flights)
data(flights)
```

- 所生成的数据格式是`tibble`。他是data.frame的现代版本，具有数据框的大多数属性，但是特别适用于大型数据集的存储和表示。

- http://tibble.tidyverse.org

# dplyr动作
1. 取行：`filter()`
2. 排序: `arrange()`
3. 取列: `select()`
4. 生成新变量: `mutate()`
5. 分组汇总: `group_by() %>% summarise()`
6. 动作连贯：` %>% `: 快捷键： ctrl + shift + M

# filter()
```{r}
dplyr::filter(flights, month ==1, day == 1)
```

base R 方法
```{r}
flights[flights$month == 1 & flights$day == 1, ]
```

# arrange()
```{r}
arrange(flights, year, month, day)
```

- 倒序：descending order
```{r}
arrange(flights, desc(arr_delay))
```

# 取列
```{r}
select(flights, year, month, day)
```

```{r}
select(flights, year:day)
```

```{r}
select(flights, -(year:day))
```

- select可以配合`starts_with()` `ends_with()`, `matches()`, `contains()`使用。
```{r}
flights %>% select(contains('dep'))
```

# 重命名
```{r}
select(flights, tail_num = tailnum)
```

```{r}
rename(flights, tail_num = tailnum)
```


# 增添新变量
```{r}
mutate(flights,
  gain = arr_delay - dep_delay,
  speed = distance / air_time * 60
)
```

- 实时变量生成

```{r}
mutate(flights,
  gain = arr_delay - dep_delay,
  gain_per_hour = gain / (air_time / 60)
)
```

- 只保留新变量
```{r}
transmute(flights,
  gain = arr_delay - dep_delay,
  gain_per_hour = gain / (air_time / 60)
)
```


# 汇总
```{r}
summarise(flights,
  delay = mean(dep_delay, na.rm = TRUE)
)
```


- 好像很多余？

- group_by() 为 summarise插上翅膀。稍后单独展示。


# 抽样

```{r}
sample_n(flights, 10)
```


- 按比例抽样
```{r}
sample_frac(flights, 0.01)
```

# 分组

```{r}
by_tailnum <- group_by(flights, tailnum)
delay <- summarise(by_tailnum,
  count = n(),
  dist = mean(distance, na.rm = TRUE),
  delay = mean(arr_delay, na.rm = TRUE))
delay <- dplyr::filter(delay, count > 20, dist < 2000)
```

使用连贯动作
```{r}
delay <- flights %>% 
    group_by(tailnum) %>% 
    summarise(count = n(),
              dist = mean(distance, na.rm = TRUE),
              delay = mean(arr_delay, na.rm = TRUE)) %>% 
    filter(count > 20, dist < 2000)
delay
```

- 根据连贯操作很容易看懂代码

```{r}
flights %>%
  group_by(year, month, day) %>%
  select(arr_delay, dep_delay) %>%
  summarise(
    arr = mean(arr_delay, na.rm = TRUE),
    dep = mean(dep_delay, na.rm = TRUE)
  ) %>%
  filter(arr > 30 | dep > 30)
```


# 多变量汇总
```{r}
daily <- group_by(flights, year, month, day)
(per_day   <- summarise(daily, flights = n()))
(per_month <- summarise(per_day, flights = sum(flights)))
(per_year  <- summarise(per_month, flights = sum(flights)))
```

# 多表合并
```{r}
flights2 <- flights %>% select(year:day, hour, origin, dest, tailnum, carrier)

flights2 %>% 
  left_join(airlines)
```
```{r}
data("weather")
weather
flights2 %>% left_join(weather)
```


# 用特定变量合并交集
```{r}
planes
flights2 %>% left_join(planes, by = "tailnum")
```

# 合并变量名称不同？
```{r}
airports
flights2 %>% left_join(airports, c("dest" = "faa"))
flights2 %>% left_join(airports, c("origin" = "faa"))
```

# 四种合并（join）方式
```{r}
df1 <- tibble(x = c(1, 2), y = 2:1)
df2 <- tibble(x = c(1, 3), a = 10, b = "a")
df1
df2
```
1. `inner_join(x, y)`: xy交集

```{r}
df1 %>% inner_join(df2)
```
2. `left_join(x, y)`, 保留x的所有观测。最为常见
```{r}
df1 %>% left_join(df2)
```

3. `right_join()`，保留y中的所有观测，等同于`left_join(y, x)`,但列的排序稍有不同。
```{r}
df1 %>% right_join(df2)
df2 %>% left_join(df1)
```
4. `full_join()` 保留x, y所有观测，用NA填充。
```{r}
df1 %>% full_join(df2)
```

# 与观测有关的join
1. `semi_join(x, y)`: 保留y中有匹配的x观测值
2. `anti_join(x, y)`：将x中与y有匹配的数据全部丢弃
```{r}
flights %>% 
  anti_join(planes, by = "tailnum") %>% 
  count(tailnum, sort = TRUE)
```

```{r}
df1 <- tibble(x = c(1, 1, 3, 4), y = 1:4)
df2 <- tibble(x = c(1, 1, 2), z = c("a", "b", "a"))
df1
df2
df1 %>% nrow()
df1 %>% inner_join(df2, by = "x")
df1 %>% semi_join(df2, by = "x")
```

# 集合操作
- `intersect(x, y)`: xy交集
- `union(x, y)`: xy并集
- `setdiff(x, y)`: x中y的补集
```{r}
(df1 <- tibble(x = 1:2, y = c(1L, 1L)))
(df2 <- tibble(x = 1:2, y = 1:2))
intersect(df1, df2)
union(df1, df2)
setdiff(df1, df2)
setdiff(df2, df1)
```

# 窗口函数 (window functions)

与mutate和filter结合使用，窗口函数可以大有作为

```{r}
library(Lahman)
batting <- Lahman::Batting %>%
  as_tibble() %>%
  select(playerID, yearID, teamID, G, AB:H) %>%
  arrange(playerID, yearID, teamID) %>%
  semi_join(Lahman::AwardsPlayers, by = "playerID")

players <- batting %>% group_by(playerID)
players
```



```{r}
# For each player, find the two years with most hits
filter(players, min_rank(desc(H)) <= 2 & H > 0)
# Within each player, rank each year by the number of games played
mutate(players, G_rank = min_rank(G))
# For each player, find every year that was better than the previous year
filter(players, G > lag(G))
# For each player, compute avg change in games played per year
mutate(players, G_change = (G - lag(G)) / (yearID - lag(yearID)))

# For each player, find all where they played more games than average
filter(players, G > mean(G))
# For each, player compute a z score based on number of games played
mutate(players, G_z = (G - mean(G)) / sd(G))
```

- 窗口函数可以让我们在行和列操作时更加自如，它们主要分为5中，先介绍两种
1. 排序和计算顺序：row_number(), min_rank(), dense_rank(), cume_dist(), percent_rank(), and ntile(). 
2. 滞后和领先操作： lead() and lag()



# 排序
```{r}
x <- c(1, 1, 2, 2, 2)

row_number(x)

min_rank(x)

dense_rank(x)

cume_dist(x)
```


```{r}
# select the top 10% of records within each group
filter(players, cume_dist(desc(G)) < 0.1)
```

- ntile() 将变量数据分为相等的n块。
```{r}
by_team_player <- group_by(batting, teamID, playerID)
by_team <- summarise(by_team_player, G = sum(G))
by_team_quartile <- group_by(by_team, quartile = ntile(G, 4))
summarise(by_team_quartile, mean(G))
```


# 领先滞后
```{r}
x <- 1:5
lead(x)
lag(x)
```


```{r}
# Compute the relative change in games played
mutate(players, G_delta = G - lag(G))
# Find when a player changed teams
filter(players, teamID != lag(teamID))
```


- 自学后三种动作，现实中用的不太多，了解滞后，可以需要的时候再查阅帮助文档。但以上操作应该烂熟于胸。











